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Information Processing

Learning Objectives • To determine the number of possible orderings of an arbitrary number of objects following certain procedures. • To learn a SET game for developing logical thinking . • To investigate the role of map colouring in representing and modelling of mathematical ideas. • To observe the Fibonacci pattern in physical and biological phenomena. • To choose the best method in finding the HCF of numbers. • To understand how information can be processed in, encryption and decryption. • To consider alternatives in shopping before making a purchase, calculate the unit price for each items and make purchase in limited budget. • To understand how to pack things eﬃciently in a given space and find the optimal solution.

Chapter 7

INFORMATION PROCESSING

Learning Objectives

• To determine the number of possible orderings of an arbitrary number of objects following certain procedures.

• To learn a SET game for developing logical thinking .

• To investigate the role of map colouring in representing and modelling of mathematical ideas.

• To observe the Fibonacci pattern in physical and biological phenomena.

• To choose the best method in finding the HCF of numbers.

• To understand how information can be processed in, encryption and decryption.

• To consider alternatives in shopping before making a purchase, calculate the unit price for each items and make purchase in limited budget.

• To understand how to pack things eciently in a given space and find the optimal solution.

Recap

Before to learn, we recall the concepts like listing, counting, pattern of Fibonacci series and calculate the unit price of the products by answering the following questions

1. Find the number of all possible triangles that can be formed from the triangle given below.

Single Triangles 5

Combination of 2 4

Combination of 3 2

Big triangle 1

Total : 12

Ans: 12

2. Use the numbers given in the figure to form a 3 x 3 magic square.

3. Convert the tree diagram into a numeric expression.

Answer: (10 × 5) + 9 × 4)

4. (i) Find the total time taken by the bus to reach from A to E via B , C and D.

(ii) Find which is the shortest route from A to E.

Solution:

(i) Route A → B → C → D → E

Time taken  (7 + 5 + 3 + 6) hrs = 21 hrs

(ii) Available routes : Time taken

(a) A → B → C → D → E  : 7 + 5 + 3 + 6 hrs = 21 hrs

(b) A → B → D → E : 7 + 4 + 6 = 17 hrs

(c) A → B → C → E  : 7 + 5 + 8 = 20 hrs

Shortest route A → B → D → E

5. Connect the Fibonacci squares through diagonals by curve from corner to corner across each square to draw a Golden Spiral.

Solution:

6. When you plan to buy a shirt, one shop offers a discount of 200 on MRP 1000 and another shop offers 15% discount on the same MRP. Where would you buy?

Solution:

Price in Ist shop = ₹ 1000 − ₹ 200 = ₹ 800

Price in IInd shop = [85/100] × 1000 = ₹ 850

In shop I.

7. Amazing park is offers a package deal of 5 entrance passes for 130. If one entrance pass normally costs 30, how much will you save by taking advantage of this special deal?

Solution:

Cost of one entrance pass = ₹ 30

Cost of 5 entrance passes = 5 × 30

= ₹  150

But special deal price = ₹  130

Amount of saving =  150 − 130 =  ₹ 20

Introduction

Success in Mathematics depends on the development of the number sense, logical thinking and cognitive skills. In this class, we find practical solutions for day to day life situations like selection procedures from various forms, colour the given map with minimum number of colours. We are also going to see Fibonacci number pattern in physical and biological phenomena and also discuss some cipher for the higher order thinking which is to do well in the competitive exams. We will also discuss how will you be a wise consumer while shopping and packing. Meanwhile we will play a game to support your mind blooming activities. All the above discussions are very helpful to you, to explore other chapters and improve your interest in Mathematics.

MATHEMATICS ALIVE - INFORMATION PROCESSING IN REAL LIFE

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